Dorais and Klyve proved that there are no further terms up to 9.7*10^14.

These primes are so named after the celebrated result of Mirimanoff in 1910 (see below) that for a failure of the first case of Fermat's Last Theorem, the exponent p must satisfy the congruence stated in the definition. Lerch (see below) showed that these primes also divide the numerator of the harmonic number H(floor((p-1)/3)). This is analogous to the fact that Wieferich primes (A001220) divide the numerator of the harmonic number H((p-1)/2). - John Blythe Dobson, Mar 02 2014